High-capacity long-haul transmission at low cost is of crucial importance to meet the ever-increasing demand in optical communications. Designing long-haul (e.g., designed for distances in excess of 1000 km) dense wavelength-division-multiplexed (DWDM) systems is a means to achieve high capacity and low cost. However, many of the current high bit rate (e.g., with data rates of 40 Gb/s) DWDM systems use a pseudo linear transmission format called return to zero (RZ) on-off keying (OOK) transmission, in which the presence or absence of light to convey information, e.g. a digital “one” is represented by the presence of an optical pulse and a “zero” is represented by the absence of a pulse. These systems suffer from various non-linear transmission penalties, such as intra-channel cross-phase modulation (XPM) and intra-channel four wave mixing (FWM), the latter of which results in the amplitude fluctuation in “1s” and the generation of ghost pulses through energy transfers from “1s” to “0s”. These effects undesirably limit the ultimate reach of the system.
While intra-channel XPM can be effectively suppressed by optimum dispersion management, intra-channel FWM remains a limiting nonlinear penalty in long-haul high-bit-rate transmission, despite various attempts that have been made to deal with that effect. For example, different signaling or modulation formats, such as return to zero (RZ), carrier-suppressed RZ (CS-RZ), chirped RZ (C-RZ), modified duo-binary, etc., have been suggested. Unfortunately, however, these attempts have not met realistic commercial needs, due, in part to problems associated not just with performance limitations, but also with expense, and implementation difficulty. For example, one approach to suppressing ghost pulse generation is to use duobinary and modified duobinary formats. However, that approach is not optimal, because the implementation of these transmission formats generally requires either complicated electronics or extra optical component hardware on the transmitter side of the transmission link.